Battery dies after car is turned off and check engine light is on

The Engine Computer detected a problem, set a diagnostic fault code, and turned the Check Engine light on to tell you. The place to start is by having the codes read. Many auto parts stores will do that for you for free, but it's important to understand that those codes will never say to replace a part or that one is defective. They only indicate the circuit or system that needs further diagnosis.

A test of the charging system may be in order to see if it is capable of delivering its rated output current. If one of the six internal diodes is bad, the common 90 amp alternator will only deliver 30 amps, and that is not enough to run the entire electrical system under all conditions. The battery will have to make up the difference until it slowly runs down over hours or days.